{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JCNFXGLQGRXXAPDW65QCERLSFI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"982c9ca7a1cfe4efd335df9485b976110cc64c1de769c0af9b7b22bb3fd31390","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T02:04:39Z","title_canon_sha256":"82c6ef6b71b679a2001724bd15db5220c8e957445ec155ca2017a3bad1ebc8d9"},"schema_version":"1.0","source":{"id":"1401.5539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5539","created_at":"2026-05-18T03:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5539v1","created_at":"2026-05-18T03:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5539","created_at":"2026-05-18T03:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"JCNFXGLQGRXX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JCNFXGLQGRXXAPDW","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JCNFXGLQ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:cc13d41ead0187d1797ef3cd2af472d39541b7c39ad9da46c6749d2700ecec99","target":"graph","created_at":"2026-05-18T03:01:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"An $hp$-discontinuous Galerkin (DG) method is applied to a class of second order linear hyperbolic integro-differential equations. Based on the analysis of an expanded mixed type Ritz-Volterra projection, {\\it a priori} $hp$-error estimates in $L^{\\infty}(L^2)$-norm of the velocity as well as of the displacement, which are optimal in the discretizing parameter $h$ and suboptimal in the degree of polynomial $p$ are derived. For optimal estimates of the displacement in $L^{\\infty}(L^2)$-norm with reduced regularity on the exact solution, a variant of Baker's nonstandard energy formulation is dev","authors_text":"Amiya K. Pani, Samir Karaa, Sangita Yadav","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T02:04:39Z","title":"A Priori $hp$-estimates for Discontinuous Galerkin Approximations to Linear Hyperbolic Integro-Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5539","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8c1b4817621803fd244db11f35473ca23171b62fd5ee5c6993663d52298b5197","target":"record","created_at":"2026-05-18T03:01:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"982c9ca7a1cfe4efd335df9485b976110cc64c1de769c0af9b7b22bb3fd31390","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T02:04:39Z","title_canon_sha256":"82c6ef6b71b679a2001724bd15db5220c8e957445ec155ca2017a3bad1ebc8d9"},"schema_version":"1.0","source":{"id":"1401.5539","kind":"arxiv","version":1}},"canonical_sha256":"489a5b9970346f703c76f7602245722a160c2922ab0882a406c87dbfb0f202c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"489a5b9970346f703c76f7602245722a160c2922ab0882a406c87dbfb0f202c3","first_computed_at":"2026-05-18T03:01:26.021740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:26.021740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XnEKiUEWFAULsUSoA64mMhQV2kBNFO+a2kOJOroF3TOHT7Lzybu44Rixg+oUonJJ2jTIWKsLIcqJFrkJejjNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:26.022485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c1b4817621803fd244db11f35473ca23171b62fd5ee5c6993663d52298b5197","sha256:cc13d41ead0187d1797ef3cd2af472d39541b7c39ad9da46c6749d2700ecec99"],"state_sha256":"7f6fba561ab4a7bd4d7f2e3807529ac76fac25a250f2a0680eea9db9c1047a0d"}